Reliability Investigation of BiCGStab and IDR Solvers for the Advection-Diffusion-Reaction Equation

Eigenvalues, singular values, and eigenvectors (15A18) Iterative numerical methods for linear systems (65F10) Linear equations (linear algebraic aspects) (15A06) Toeplitz, Cauchy, and related matrices (15B05)

Related Items (1)

krylov-adr

Uses Software

Matlab
BiCGstab
COMSOL
Eigen
IDRStab

Cites Work

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BiCGstab($l$) and other hybrid Bi-CG methods
BiCGstab($l$) for linear equations involving unsymmetric matrices with complex spectrum
Newton-Krylov methods applied to a system of convection-diffusion-reaction equations
A block version of BiCGSTAB for linear systems with multiple right-hand sides
Reliable updated residuals in hybrid Bi-CG methods
On parameter choice and iterative convergence for stabilised discretisations of advection-diffusion problems
A variant of IDRstab with reliable update strategies for solving sparse linear systems
Finite Elements and Fast Iterative Solvers
Exploiting BiCGstab($\ell$) Strategies to Induce Dimension Reduction
Numerical study in stochastic homogenization for elliptic partial differential equations: Convergence rate in the size of representative volume elements
Necessary and Sufficient Conditions for the Existence of a Conjugate Gradient Method
Recycling BiCGSTAB with an Application to Parametric Model Order Reduction
On Optimal Short Recurrences for Generating Orthogonal Krylov Subspace Bases
IDR(s): A Family of Simple and Fast Algorithms for Solving Large Nonsymmetric Systems of Linear Equations
GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
Bi-CGSTAB: A Fast and Smoothly Converging Variant of Bi-CG for the Solution of Nonsymmetric Linear Systems
Lanczos Methods for the Solution of Nonsymmetric Systems of Linear Equations
Residual-Minimizing Krylov Subspace Methods for Stabilized Discretizations of Convection-Diffusion Equations
Convergence analysis of Krylov subspace methods
Iterative Krylov Methods for Large Linear Systems
A Novel Method for Solving Time-Dependent 2D Advection-Diffusion-Reaction Equations to Model Transfer in Nonlinear Anisotropic Media
Tridiagonal Toeplitz matrices: properties and novel applications
Introduction to matrix analysis and applications

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